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An Efficient Rational Secret Sharing Scheme Based on the Chinese Remainder Theorem (Revised Version)
The design of rational cryptographic protocols is a recently created research area at the intersection of cryptography and game theory. At TCC\u2710, Fuchsbauer \emph{et al.} introduced two equilibrium notions (computational version of strict Nash equilibrium and stability with respect to trembles) offering a computational relaxation of traditional game theory equilibria. Using trapdoor permutations, they constructed a rational -out-of sharing technique satisfying these new security models. Their construction only requires standard communication networks but the share bitsize is for security against a single deviation and raises to to achieve -resilience where is a security parameter. In this paper, we propose a new protocol for rational -out-of secret sharing scheme based on the Chinese reminder theorem. Under some computational assumptions related to the discrete logarithm problem and RSA, this construction leads to a -resilient computational strict Nash equilibrium that is stable with respect to trembles with share bitsize . Our protocol does not rely on simultaneous channel. Instead, it only requires synchronous broadcast channel and synchronous pairwise private channels